Standardization methods in activation analysis with charged particles are studied critically. Several approximate standardization
methods that do not require knowledge of the excitation function are compared with the “numerical integration method” using
excitation function data from the literature. It is shown that these methods yield accurate results if the threshold energy
of the considered reaction is high and if sample and standard have a comparable Z value. A method that gives a rapid estimate
of the maximum possible error is also presented. It is shown that for the “numerical integration method” the accuracy of the
excitation function data has only a small influence on the overall accuracy. The influence of the accuracy of stopping power
data and of possible deviations from Bragg's rule for light element standards is also considered.
Authors:Jorge Capela, Marisa Capela, and Clóvis Ribeiro
The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian
quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical
integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized
in order to obtain approximations with the maximum of accurate.
Authors:P. Suarez, S. Guevara, M. Arribére, and A. Kestelman
The235U fission neutron spectrum averaged cross section for the50Ti(n,)47Ca reaction was experimentally determined by irradiation of titanium with reactor neutrons. A value of (9.7±1.1) b was found for this cross section, using (307±11) b for the48Ti(n,p)48Sc spectrum-averaged cross section that was used as a standard. The50Ti(n,)47Ca spectrum-averaged cross section was also semiempirically evaluated by numerically integrating, through the ENDF/B-V representation of the235U fission neutron spectrum, the available experimental differential cross section data.
A new method of calculation of parameters of enthalpy relaxation models is proposed. Regression analysis treatment compares the experimental and calculated values of relaxation enthalpy. The experimental values of relaxation enthalpy are obtained by numerical integration of the difference between the two DSC curves. Contrary to the overall shape of the DSC curve the integral values are not affected by particular heat flow conditions during the DSC experiment. The Narayanaswamy's numerical model based on the Kohlrausch—William—Watts relaxation function was used to calculate the theoretical values of relaxation enthalpy. The application of the proposed method on the DSC experimental data of enthalpy relaxation of As2Se3 is shown.
Authors:T. Wanjun, L. Yuwen, Z. Hen, W. Zhiyong, and W. Cunxin
A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic
parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical
calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with
several published approximate formulae, this new one is much superior to all other approximations and is the most suitable
solution for the evaluation of kinetic parameters from TG experiments.
The mathematical evaluation of the activation
energy, E, of non-isothermal degradation
reactions is usually made using the Ozawa/Flynn–Wall isoconversion principle
and involves the numerical resolution of a set of integrals without closed
form solution, which are solved by polynomial approximation or by numeric
integration. In the present work, the isoconversion principle, originally
described and maintained until now as an algebraic problem, was written as
a set of ordinary differential equations (ODEs). The individual ODEs obtained
are integrated by numeric methods and are used to estimate the activation
energy of simulated examples. A least square error (LSE) objective function
using the introduced ODEs was written to deal with multiple heating rate CaCO3
thermal decomposition TG experiments.
Authors:Hai-Qing Zhang, Bang-Fa Ni, Wei-Zhi Tian, Gui-Ying Zhang, Dong-Hui Huang, Cun-Xiong Liu, Cai-Jin Xiao, Peng Nie, and Hong-Chao Sun
An expression of γ-ray efficiency for large samples is proposed based on numerical integration of efficiencies over compositional
point sources. The widely used expression on radial variation of HPGe efficiency for point source originally proposed by Noguchi
et al. (Int J Appl Radiat Isot 32:17–22, 1980 [<cite>1</cite>]) was amended and a new expression was proposed. A comparison between the two expressions indicates that the newly proposed
expression brings about an obvious improvement, and Self-absorption correction for a voluminous source is also given out by
using the EID principle. The functional relationship between HPGe efficiency for γ-rays from a point source and the spatial
position of the source was established. The results of this study can be applied in order to determine γ attenuation effects
of unknown bulky samples with various shapes and materials.